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2. (20 pts) The following price demand for three goods x, y and z are given:...
Cramer's Rule: 5. Use Cramer's Rule to find x,y and z for the following system of...
Cramer's Rule: 5. Use Cramer's Rule to find x,y and z for the following system of equations. X 2 7x + 2y - z= -1 ។ 6x + 5y + z = 16 -5x - 4y + 3z = -5 2 : 2 a. Write the coefficient matrix first for the system above. Call it matrix D. 7 2 5 L-8-4 3 1 14 ] = 0 b. Find the determinant of the coefficient matrix (det(D)).
A multiplant monopoly produces the quantities x, y, and z in the three plants that it...
A multiplant monopoly produces the quantities x, y, and z in the three plants that it operates and faces the profit function Profit = -24 + 839 x + 837 y + 835 2 - 5.05 x2.5.03 y2.5.02 z2 - 10 xy - 10 xz - 10 yz and The optimum values of x, y and z are respectively. [NOTE: Please use the whole number and do not use any decimal point for the optimum values of x, y, and...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+y2- 1 1. (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x -0.9y-z 2 x2+ y2- 0.9.
Solve the following problem...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+ y2- 1 (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x-0.9y-z =2 x2+y2- 0.9
Solve the following problem using Lagrange...
Utility Function: U = ln (x) + ln (z) Budget Constraint: 120 = 2x + 3z...
Utility Function: U = ln (x) + ln (z) Budget Constraint: 120 = 2x + 3z (a) Find the optimal values of x and z (b) Explain in words the idea of a compensating variation for the case where the budget constraint changed to 120 = 2x + 5z Problem 4 (a) Derive the demand functions for the utility function (b) Let a = 2, b = 5, px = 1, pz = 3, and Y = 75. Find the...
2. Consider the function f : R2 → R2 given by. (x,y) (a) Compute the Df(x, y) (b) List every vect...
2. Consider the function f : R2 → R2 given by. (x,y) (a) Compute the Df(x, y) (b) List every vector r e R2 such that Df(ri, r2) 0. What can we say about the tangent plane to the surface of the graph at (ri,2,f(r1, r2))? (c) How do you know that the Hessian, Df(x, y) is necessarily symmetric? Recall that t,y D2 f(x,y) , y) (d) What are the eigenva of D2f(r1,r2) for each root of the gradient that...
A household's utility function is given by U(x, y, z) = 6 In x + 9...
A household's utility function is given by U(x, y, z) = 6 In x + 9 ln y + 15 In z, where x,y and z are the quantities of products X, Y and Z respectively, consumed by the household each month. The prices per unit for these three goods are px = $6, Py = $15 and pz = $24, respectively. The household's monthly budget for these goods is B = $4800. Question 11 2 pts This continues the...
2. Find the augmented matrix of the linear system X – y + z = 7...
2. Find the augmented matrix of the linear system X – y + z = 7 x + 3y + 3z = 5 X – Y – 2z = 4 Use Gauss-Jordon elimination to transform the augmented matrix to its reduced row- echelon form. Then find the solution or the solution set of the linear system.
experiment and records the following observations: 2. An engineer conducts an 3 2 1 X 9.3...
experiment and records the following observations: 2. An engineer conducts an 3 2 1 X 9.3 1.2 3.6 y model of the form, y = ax, find the optimal least squares Assuming that the recorded data obeys estimates of "a and b". Also, using the above estimated values of "a and b," find a predicted value of y for x 5. a [Note: You need not check the Hessian Matrix for sufficiency condition]. Hint: First convert the given model to...
experiment and records the following observations: 2. An engineer conducts an 3 2 1 X 9.3...
experiment and records the following observations: 2. An engineer conducts an 3 2 1 X 9.3 1.2 3.6 y model of the form, y = ax, find the optimal least squares Assuming that the recorded data obeys estimates of "a and b". Also, using the above estimated values of "a and b," find a predicted value of y for x 5. a [Note: You need not check the Hessian Matrix for sufficiency condition]. Hint: First convert the given model to...
Cramer's Rule: 5. Use Cramer's Rule to find x,y and z for the following system of equations. X 2 7x + 2y - z= -1 ។ 6x + 5y + z = 16 -5x - 4y + 3z = -5 2 : 2 a. Write the coefficient matrix first for the system above. Call it matrix D. 7 2 5 L-8-4 3 1 14 ] = 0 b. Find the determinant of the coefficient matrix (det(D)).
A multiplant monopoly produces the quantities x, y, and z in the three plants that it operates and faces the profit function Profit = -24 + 839 x + 837 y + 835 2 - 5.05 x2.5.03 y2.5.02 z2 - 10 xy - 10 xz - 10 yz and The optimum values of x, y and z are respectively. [NOTE: Please use the whole number and do not use any decimal point for the optimum values of x, y, and...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+y2- 1 1. (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x -0.9y-z 2 x2+ y2- 0.9.
Solve the following problem...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+ y2- 1 (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x-0.9y-z =2 x2+y2- 0.9
Solve the following problem using Lagrange...
2. Consider the function f : R2 → R2 given by. (x,y) (a) Compute the Df(x, y) (b) List every vector r e R2 such that Df(ri, r2) 0. What can we say about the tangent plane to the surface of the graph at (ri,2,f(r1, r2))? (c) How do you know that the Hessian, Df(x, y) is necessarily symmetric? Recall that t,y D2 f(x,y) , y) (d) What are the eigenva of D2f(r1,r2) for each root of the gradient that...
A household's utility function is given by U(x, y, z) = 6 In x + 9 ln y + 15 In z, where x,y and z are the quantities of products X, Y and Z respectively, consumed by the household each month. The prices per unit for these three goods are px = $6, Py = $15 and pz = $24, respectively. The household's monthly budget for these goods is B = $4800. Question 11 2 pts This continues the...
2. Find the augmented matrix of the linear system X – y + z = 7 x + 3y + 3z = 5 X – Y – 2z = 4 Use Gauss-Jordon elimination to transform the augmented matrix to its reduced row- echelon form. Then find the solution or the solution set of the linear system.
experiment and records the following observations: 2. An engineer conducts an 3 2 1 X 9.3 1.2 3.6 y model of the form, y = ax, find the optimal least squares Assuming that the recorded data obeys estimates of "a and b". Also, using the above estimated values of "a and b," find a predicted value of y for x 5. a [Note: You need not check the Hessian Matrix for sufficiency condition]. Hint: First convert the given model to...
experiment and records the following observations: 2. An engineer conducts an 3 2 1 X 9.3 1.2 3.6 y model of the form, y = ax, find the optimal least squares Assuming that the recorded data obeys estimates of "a and b". Also, using the above estimated values of "a and b," find a predicted value of y for x 5. a [Note: You need not check the Hessian Matrix for sufficiency condition]. Hint: First convert the given model to...
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